Besanko and Braeutigam, CH 13
Western University
| Market Structure | Number of Firms | Type of Product | Control Over Price | Examples |
|---|---|---|---|---|
| Perfect Competition | Many | Homogeneous | None | Agriculture (US) |
| Monopolistic Competition | Many | Differentiated | Some | Retail stores |
| Oligopoly | Few | Homogeneous or Differentiated | Some to Significant | Banking-Big 5 (CA) |
| Monopoly | One | Unique | Significant | Utilities |
| Dominant Firm | One dominant, Many small | Homogeneous | Significant by dominant firm | US: Scotch Tape (3M) |
Four-Firm Concentration Ratio (4CR): The share of industry sales revenue accounted for by the four firms with the largest sales revenue in the industry
Herfindahl–Hirschman Index (HHI): The sum of the squares of the market share of each firm in the industry (\(0 \le HHI \le 10,000\))
| Market Structure | 4CR | HHI |
|---|---|---|
| Perfect Competition | Low | Low |
| Olygopoly | Intermediate | Intermediate |
| Monopoly | 100 | 10,000 |
When choosing output, each firm will act as a monopolist relative to its residual demand
Firm 1 maximizes its profit by choosing \(Q_1\) that maximizes: \[ \pi_1=P(Q_1+Q_2^e)⋅Q_1−C(Q_1) \]
Best Response: For any given belief about the output of firm 2, \(Q^e_2\), there is an optimal choice of output for firm 1, \[ Q_1=BR_1(Q^e_2) \]
The best response function for Firm 1, \(BR_1(Q_2^e)\), is derived by setting: \[ \frac{\partial \pi_1}{\partial Q_1} = 0 \]
Example with Linear Demand: Assuming \(P(Q) = a - b(Q_1 + Q_2)\) and constant marginal cost \(MC = c\), the reaction functions can be simplified as: \[ \begin{aligned} Q_1= \frac{a - c}{2b} - \frac{Q_2^e}{2} \;;\; Q_2= \frac{a - c}{2b} - \frac{Q_1^e}{2} \end{aligned} \]
Reaction Function: Illustrates graphically a firm’s best response output for each possible output of the other firm’s output
Cournot Equilibrium for Two Firms: Occurs where the reaction curves of Firm 1 and Firm 2 intersect.
Equilibrium Output: Solving the system of equations given by the reaction functions yields the equilibrium outputs for both firms: \[ Q_1^* = Q_2^* = \frac{a - c}{3b} \] and the total market output is: \[ Q^* = Q_1^* + Q_2^* = \frac{2(a - c)}{3b} \]
In the Cournot equilibrium both firms fully understand their interdependence and have confidence in each other’s rationality
By independently maximizing their own profits, firms produce more total output than they would if they collusively maximized industry profits (Monopoly).
For \(N\) identical firms, each firm \(i\) will produce \[ Q^*_i = \frac{1}{N+1}\frac{a - c}{b} \]
Total market output and market price will be \[ Q^*=\sum_i Q^*_i = \frac{N}{N+1}\frac{(a - c)}{b} \] \[ P^*=a-b\left(\frac{N}{N+1}\frac{(a - c)}{b} \right) = \frac{a+Nc}{(N+1)} \]
| Market Structure | \(N\) | Optimal Firm Output \(Q^*_i\) | Total Market Output \(Q^*\) | Market Price \(P^*\) |
|---|---|---|---|---|
| Monopoly | 1 | \(\frac{a - c}{2b}\) | \(\frac{a - c}{2b}\) | \(\frac{a + c}{2}\) |
| Cournot Duopoly | 2 | \(\frac{a - c}{3b}\) | \(\frac{2(a - c)}{3b}\) | \(\frac{(a + 2c)}{3}\) |
| Perfect Competition | \(\infty\) | 0 (virtually) | \(\frac{a - c}{b}\) | \(c\) |